Anharmonic phonon energies in rare-gas solids derived by path-integral simulations

Abstract

Vibrational properties of rare-gas solids are studied as a function of temperature and pressure by path-integral Monte Carlo simulations with a Lennard-Jones potential model. The calculation of the static susceptibility tensor, that represents the linear response of the equilibrium system to vanishingly small forces on the atomic nuclei, leads to a nonperturbative approximation of the crystal phonons. The intrinsic anharmonicity of vibrational modes is quantified by comparison to harmonic phonon energies calculated at the equilibrium volume of the solid. Results obtained for longitudinal and transverse phonon energies at the boundary of the Brillouin zone, as well as elastic constants estimated from the propagation velocity of selected phonons, are compared to available experimental data for solid Ne and Ar. The studied temperatures cover a range from $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ to the triple point of the rare-gas solids, while the largest studied pressures amount to about $40\phantom{\rule{0.3em}{0ex}}\mathrm{kbar}$, that corresponds roughly to the validity limit of the employed potential model.